Re: A ball in a rotating dish (was Hot air rising ...)

[Robert A Cohen <bbq@ESU.EDU>]

I'm glad to see that my posts are read!  :)

First, I thank Bob for pointing out my error when I said...

> > 2. First some background...An object experiences a coriolis force when its
> > distance from the earth's axis changes.

This is not correct, as Bob astutely points out.  An object experiences a
coriolis force when its velocity has a component that is not parallel to
the axis (w x v).  That is why the ball, when rolling down a board
oriented parallel to the earth's axis, will not experience a coriolis
force.  My answer is correct, but my explanation was not complete.

Second, regarding Brian and Leigh's concern about my answer to the first
question...

> 1. The winds do not "feel" the centrifugal force because ... the normal
> force (of the surface) has a slight centripetal component that cancels out
> the centrifugal force.  In other words, we define a horizontal surface as
> that surface for which there is no horizontal forces on an object at rest.
> That is, a horizontal surface is *not* the surface of a sphere.  If it
> was, everyone would be leaning slightly poleward (to counteract the
> centrifugal force) just as someone leans toward the center of the circle
> when walking in a circle.

I should've placed the question in context.  Some people demonstrate the
coriolis force by rolling a ball along a rotating surface, such as a
record player.  On such a surface, the ball will be influenced by both the
coriolis force and the centrifugal force, not the coriolis force alone.

The question then becomes why is it that we don't consider the centrifugal
force when dealing with the winds if both affect the ball on a rotating
turntable.  Note: when I say the centrifugal force in this context, I mean
the centrifugal force that results due to the earth's rotation, not that
which results when winds are following curved paths (as in circulations).
I am also not considering special cases, where the relative speed of the
wind (relative to the earth's surface) approaches the absolute speed of
the surface (relative to the axis).  All I am trying to address is why a
ball on a rotating surface acts differently than a ball on the earth's
surface.

In that vein, Brian writes...

>  Coriolis effect is dynamic - it affects objects in motion. I am not
> comfortable with the assertion that the normal force has a centripetal
> component which counters a centrifugal force.

How about the following rewording of my explanation?  We can define local
vertical as being perpendicular to the orientation of a plumb bob at rest.
The top of the plumb bob is oriented poleward, which provides the
centipetal force on the plumb bob needed for it to move around the earth's
axis.  Local vertical does not point towards the center of the earth.  If
it did, we would have to include a "centrifugal" force to account for why
the bottom of the plumb bob points away from the axis.

In order to remove the "centrifugal" force from the ball on the record
player, we would have to curve the surface of the record player into the
shape of a bowl (see header) such that the normal force on the ball (due
to the surface of the bowl) exactly counteracts the centrifugal force.
This is essentially what our definition of "horizontal" on the earth
accomplishes.

And Leigh adds...

> I won't go into detail, but I think your first question (and
> consequently your answer) are ill conceived. You are raising the specter
> of the mysterious "centripetal force" (I know, you said "component")
> again.  If you don't think this confuses students and high school
> teachers then you haven't been teaching very long.

You are right and wrong.  I *do* think this confuses students and I
*haven't* been teaching very long (at least not long when compared to
you).  On the other hand, while I have found that students and teachers
are *not* confused by the traditional "ball on a turntable" demo of the
coriolis force, I think they *should* be, because it doesn't really
demonstrate the coriolis force.

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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